Influential Language Data Selection via Gradient Trajectory Pursuit

Curating a desirable dataset for training has been the core of building highly capable large language models (Touvron et al., 2023; Achiam et al., 2023; Team et al.,2024). Gradient influence scores (Pruthi et al., 2020; Xia et al., 2024) are shown to be correlated with model performance and are commonly used as the criterion for data selection. However, existing methods are built upon either individual sample rankings or inefficient matching process, leading to suboptimal performance or scaling up issues.In this paper, we propose Gradient Trajectory Pursuit (GTP), an algorithm that performs pursuit of gradient trajectories via jointly selecting data points under an L0-norm regularized objective. The proposed algorithm highlights: (1) joint selection instead of independent top-k selection, which automatically de-duplicates samples; (2) higher efficiency with compressive sampling processes, which can be further sped up using a distributed framework. In the experiments, we demonstrate the algorithm in both in-domain and target-domain selection benchmarks and show that it outperforms top-k selection and competitive algorithms consistently, for example, our algorithm chooses as low as 0.5% data to achieve full performance on the targeted instruction tuning tasks